reesehs_OriginalHomeworkCode_03

#height
height <- (d$height) #takes data from the column height in the data from d
mh <- mean(height) #takes the mean of the height data
sqrt(sum((height - mean(height))^2)/length(height)) #calculates the standard deviation of height data

#weight
weight <- (d$weight)
mw <- mean(weight)
sqrt(sum((weight - mean(weight))^2)/length(weight))

#age
age <- (d$age)
ma <- mean(age)
sqrt(sum((age - mean(age))^2)/length(age))

#number of zombies killed
zk <- (d$zombies_killed)
mzk <- mean(zk)
sqrt(sum((zk - mean(zk))^2)/length(zk))

#years of education
yoedu <- (d$years_of_education)
myoedu <- mean(yoedu)
sqrt(sum((yoedu - mean(yoedu))^2)/length(yoedu))

library(ggplot2)

p <- ggplot(data = d, aes(x = gender, y = height)) #create graph with data from gender in x axis and data from height in y axis, all data is taken from the data frame d
p <- p + geom_boxplot()  #create boxplot
p <- p + theme(axis.text.x = element_text(angle = 90)) #shift angle of x axis
p <- p + ylab("Height") #labels y axis
p

w <- ggplot(data = d, aes(x = gender, y = weight))
w <- w + geom_boxplot() 
w <- w + theme(axis.text.x = element_text(angle = 90))
w <- w + ylab("Weight")
w

a <- ggplot(data = d, aes(x = gender, y = age))
a <- a + geom_boxplot() 
a <- a + theme(axis.text.x = element_text(angle = 90))
a <- a + ylab("Age")
a

zn <- ggplot(data = d, aes(x = gender, y = zk))
zn <- zn + geom_boxplot() 
zn <- zn + theme(axis.text.x = element_text(angle = 90))
zn <- zn + ylab("Number of Zombies Killed")
zn

ey <- ggplot(data = d, aes(x = gender, y = yoedu))
ey <- ey + geom_boxplot() 
ey <- ey + theme(axis.text.x = element_text(angle = 90))
ey <- ey + ylab("Years of Education")
ey

hg <- ggplot(data = d, aes(x = age, y = height)) + geom_point() + xlab("age") + ylab("height") + theme(legend.position = "bottom", legend.title = element_blank()) #creates scatter plot ggplot using data from age and height(in data frame d) with x and y axises labeled
hg 

wg <- ggplot(data = d, aes(x = age, y = weight)) + geom_point() + xlab("age") + ylab("weight") + theme(legend.position = "bottom", legend.title = element_blank()) 
wg

# As age increases so do both weight and height. The scatter plots demonstrate an upward slope that shows this relationship. 

hist(height, probability = TRUE) #creates histogram using height data and comparing the probability

qqnorm(height, main = "Normal QQ plot random normal variables")  #creates qqnorm graph to test normal distribution
qqline(height, col = "gray") #create line that is the normal distribution

hist(weight, probability = TRUE)

qqnorm(weight, main = "Normal QQ plot random normal variables")
qqline(weight, col = "gray")

hist(age, probability = TRUE)

qqnorm(age, main = "Normal QQ plot random normal variables")
qqline(age, col = "gray")

hist(zk, probability = TRUE)

qqnorm(zk, main = "Normal QQ plot random normal variables")
qqline(zk, col = "gray")

hist(yoedu, probability = TRUE)

qqnorm(yoedu, main = "Normal QQ plot random normal variables")
qqline(yoedu, col = "gray")

# Both number of zombies killed and years of education are not normally distributed. I am not sure what common distribution they are drawn to. 

#sample(d, 30, replace = FALSE)
#in this case the length of d is only 10 so this doesn't work

#height
hs <- sample(height, 30, replace = FALSE) #takes a random sample of 30 from the height dataset
mhs <- mean(hs) #takes mean of the 30 samples
sdhs <- sd(hs) # I'm honestly a little confused on the difference between sample standard deviation and standard error? 
hsse <- sdhs/sqrt(30) #takes standard error of the 30 samples
lower <- mh - qnorm(1 - 0.05/2) * hsse  
upper <- mh + qnorm(1 - 0.05/2) * hsse 
ci <- c(lower, upper) #caclulates the confidence interval
ci

#weight
ws <- sample(weight, 30, replace = FALSE)
ws

mws <- mean(ws)
sdws <- sd(ws)
sdws

sews <- sdws/sqrt(30)
sews

lower <- mw - qnorm(1 - 0.05/2) * sews  # (1-alpha)/2 each in the upper and lower tails of the distribution
upper <- mw + qnorm(1 - 0.05/2) * sews  # (1-alpha)/2 each in the upper and lower tails of the distribution
ci <- c(lower, upper)
ci

#age
as <- sample(age, 30, replace = FALSE)
as

mas <- mean(as)
sdas <- sd(as)
sdas

seas <- sdas/sqrt(30)
seas

lower <- ma - qnorm(1 - 0.05/2) * seas  # (1-alpha)/2 each in the upper and lower tails of the distribution
upper <- ma + qnorm(1 - 0.05/2) * seas  # (1-alpha)/2 each in the upper and lower tails of the distribution
ci <- c(lower, upper)
ci

#for both zombies killed and years of education because they both were not normal distributions the central limit theorem will be used because these are samples and it can simulate a normal distribution - but honestly I don't know how to do that so any help would be appreciated! Or maybe is it supposed to be a t distribution? 

#zombies killed
zks <- sample(zk, 30, replace = FALSE)
zks

mzks <- mean(zks)
sdzks <- sd(zks)
sdzks

sezks <- sdzks/sqrt(30)
sezks

lower <- mzk - qnorm(1 - 0.05/2) * sezks  # (1-alpha)/2 each in the upper and lower tails of the distribution
upper <- mzk + qnorm(1 - 0.05/2) * sezks  # (1-alpha)/2 each in the upper and lower tails of the distribution
ci <- c(lower, upper)
ci

#years of education
edus <- sample(yoedu, 30, replace = FALSE)
edus

medus <- mean(edus)
sdedu <- sd(edus)
sdedu

seedu <- sdedu/sqrt(30)
seedu

lower <- myoedu - qnorm(1 - 0.05/2) * seedu  # (1-alpha)/2 each in the upper and lower tails of the distribution
upper <- myoedu + qnorm(1 - 0.05/2) * seedu  # (1-alpha)/2 each in the upper and lower tails of the distribution
ci <- c(lower, upper)
ci

#height
hs2 <- NULL  # sets up a dummy variable
n <- 30 #number of samples 
for (i in 1:99) {
    hs2[[i]] <- mean(sample(height, n, replace = FALSE))
} #draws 99 samples with 30 random numbers from height data set and takes the mean of each sample set
hs2 <- append(hs2, mhs, after = 99) #adds the mean from question 5 to the list
hs2 <- unlist(hs2) #unlist the variable
mean(hs2) # takes the mean

sd(hs2) #takes the standard deviation

#weight
ws2 <- NULL
for (i in 1:99) {
    ws2[[i]] <- mean(sample(weight, n, replace = FALSE))
}
ws2 <- append(ws2, mws, after = 99)
ws2 <- unlist(ws2)
mean(ws2)

sd(ws2)

#age
as2 <- NULL
for (i in 1:99) {
    as2[[i]] <- mean(sample(age, n, replace = FALSE))
}
as2 <- append(as2, mas, after = 99)
as2 <- unlist(as2)
mean(as2)

sd(as2)

#zombies killed
zks2 <- NULL
for (i in 1:99) {
    zks2[[i]] <- mean(sample(zk, n, replace = FALSE))
}
zks2 <- append(zks2, mzks, after = 99) #adds the mean from the sample in question 5 
zks2 <- unlist(zks2)
mean(zks2)

sd(zks2)

#years of education
yedus2 <- NULL
for (i in 1:99) {
    yedus2[[i]] <- mean(sample(yoedu, n, replace = FALSE))
}
yedus2 <- append(yedus2, medus, after = 99)
yedus2 <- unlist(yedus2)
mean(yedus2)

sd(yedus2)

#height
hist(hs2, probability = TRUE) #create histogram from sample distribution calculated in chunk above

qqnorm(hs2, main = "Normal QQ plot random normal variables")  #plots qqnorm graph based of hs2 data
qqline(hs2, col = "gray") #plot qqline 

#weight
hist(ws2, probability = TRUE)

qqnorm(ws2, main = "Normal QQ plot random normal variables")
qqline(ws2, col = "gray")

#age
hist(as2, probability = TRUE)

qqnorm(as2, main = "Normal QQ plot random normal variables")
qqline(as2, col = "gray")

#number of zombies killed
hist(zks2, probability = TRUE)

qqnorm(zks2, main = "Normal QQ plot random normal variables")
qqline(zks2, col = "gray")

#years of education
hist(yedus2, probability = TRUE)

qqnorm(yedus2, main = "Normal QQ plot random normal variables")
qqline(yedus2, col = "gray")

# Most of the variables are normally distributed, of course this is a little variation like in the number of zombies killed. But compared to the original histograms of the population the qqline graph seem to follow the line more, especially in years of education and number of zombies killed, which were originally not.